T-SQL BFS center node of undirected graph

Question

I am trying to answer this question by using a breadth-first search from each node of the graph represented by the tables mapSolarSystems and mapSolarSystemJumps in the data dump at http://community.eveonline.com/community/toolkit.asp (important parts of schema below) in order to find the node with the lowest average edge count to all points on the subgraph of nodes with security >= 0.45.

I managed to hack together this beauty of T-SQL from various tutorials across the web. Sadly, although I managed to get it to function, I am not confident that it is correct. I've never created quite such a complicated piece of SQL before.

At the same time, I would like some assistance with idiomatic T-SQL - looks like CapWords for identifiers, usp_ for stored procedures, BEGIN always on new line. I've tried to take the worst offenders out of the first working version of the code at http://gaming.stackexchange.com/a/103876/9760 - things which I can spot. I was able to reduce the execution time to 4:21 minutes from 7:01 minutes in the process.

My priorities are:

1. Correctness vetting or fixed
2. Readability / Clarity (eg, idomatic)
3. Execution speed

T-SQL:

CREATE PROCEDURE dbo.usp_Eve_BFS
AS
BEGIN
    SET XACT_ABORT ON
    BEGIN TRAN
    SET NOCOUNT ON;

    CREATE TABLE #Result (Id int NOT NULL PRIMARY KEY, Name nvarchar(100), Average int, Maximum int)
    INSERT INTO #Result (Id, Name) SELECT solarSystemID, solarSystemName FROM mapSolarSystems WHERE security >= 0.45

    DECLARE @StartNode int
    DECLARE c CURSOR FOR SELECT Id FROM #Result
    OPEN c
    FETCH NEXT FROM c INTO @StartNode

    WHILE @@FETCH_STATUS=0
    BEGIN
        CREATE TABLE #Discovered (Id int NOT NULL PRIMARY KEY, Parent int NULL, Depth int)
        INSERT INTO #Discovered (Id, parent, depth) VALUES (@StartNode, NULL, 0)

        WHILE @@ROWCOUNT > 0
        BEGIN
            INSERT INTO #Discovered (Id, Parent, Depth)
            SELECT toSolarSystemID, MAX(fromSolarSystemID), MIN(Depth) + 1
            FROM #Discovered d JOIN mapSolarSystemJumps ON d.Id = fromSolarSystemID
            JOIN #Result ON (mapSolarSystemJumps.toSolarSystemID = #Result.Id)
            WHERE toSolarSystemID NOT IN (SELECT Id From #Discovered)
            AND Depth = ( -- make sure the fromSolarSystemID matches the MIN(depth)!
                SELECT MIN(Depth) FROM #Discovered d JOIN mapSolarSystemJumps ON d.Id = fromSolarSystemID
                JOIN #Result ON (mapSolarSystemJumps.toSolarSystemID = #Result.Id)
                WHERE toSolarSystemID NOT IN (SELECT Id From #Discovered)
            )
            GROUP BY toSolarSystemID
        END;

        WITH BacktraceCTE(Id, Depth) AS
        (
            SELECT Id, Depth
            FROM #Discovered d
            WHERE d.Id = @StartNode
        UNION ALL
            SELECT d.Id, d.Depth
            FROM #Discovered d JOIN BacktraceCTE cte ON d.Parent = cte.Id
        )
        UPDATE #Result
        SET Average = a.Average, Maximum = a.Maximum
        FROM (SELECT AVG(Depth) AS Average, MAX(Depth) AS Maximum FROM BacktraceCTE) AS a
        WHERE #Result.Id = @StartNode

        DROP TABLE #Discovered

        FETCH NEXT FROM c INTO @StartNode
    END

    SELECT * FROM #Result ORDER BY Average, Maximum;
    DROP TABLE #Result

    COMMIT TRAN
    RETURN 0
END

The basic shape came from http://hansolav.net/sql/graphs.html#bfs.

Edit: mapSolarSystems relevant columns:

regionID    int
constellationID int
solarSystemID   int
solarSystemName nvarchar(100)
security    float

mapSolarSystems relevant indexes:

mapSolarSystems_IX_constellation    nonclustered located on PRIMARY constellationID
mapSolarSystems_IX_region   nonclustered located on PRIMARY regionID
mapSolarSystems_IX_security nonclustered located on PRIMARY security
mapSolarSystems_PK  clustered, unique, primary key located on PRIMARY solarSystemID

mapSolarSystemJumps relevant columns:

fromRegionID    int
fromConstellationID int
fromSolarSystemID   int
toSolarSystemID int
toConstellationID   int
toRegionID  int

mapSolarSystemJumps relevant indexes:

mapSolarSystemJumps_IX_fromConstellation    nonclustered located on PRIMARY fromConstellationID
mapSolarSystemJumps_IX_fromRegion   nonclustered located on PRIMARY fromRegionID
mapSolarSystemJumps_PK  clustered, unique, primary key located on PRIMARY fromSolarSystemID, toSolarSystemID